Exotic Localized Vector Waves in a Two-Component Nonlinear Wave System

  • Ling Xu
  • Deng-Shan WangEmail author
  • Xiao-Yong Wen
  • Yao-Lin Jiang


A new two-component nonlinear wave system is studied by the generalized perturbation (\(n,N\hbox {-}n\))-fold Darboux transformation, and various exotic localized vector waves are found. Firstly, the modulational instability is investigated to reveal the mechanism of appearance of rogue waves. Then based on the N-fold Darboux transformation, the generalized perturbation (\(n,N\hbox {-}n\))-fold Darboux transformation is constructed to solve this two-component nonlinear wave system for the first time. Finally, two types of plane-wave seed solutions are selected to explore the localized vector wave solutions such as vector periodic wave solutions, vector breather solutions, vector rogue wave solutions and vector interaction solutions. It is found that there are both localized bright–dark vector waves and bright–bright vector waves in this system, which have not been reported before.


Modulational instability (\(n, N\hbox {-}n\) )-fold Darboux Localized vector waves Rogue waves 

Mathematics Subject Classification

37K10 37K15 37K40 



The authors would like to express their gratitude to Prof. Lichen Zhao and the members of the research group for the valuable suggestions on this paper. This work is supported by National Natural Science Foundation of China under Grant No. 11971067, Beijing Natural Science Foundation under Grant No. 1182009, the International Science and Technology Cooperation Program of Shaanxi Key Research Development Plan under Grant No. 2019KWZ-08, Qin Xin Talents Cultivation Program (QXTCP A201702 and QXTCP B201704) of Beijing Information Science and Technology University, and the Beijing Great Wall Talents Cultivation Program under Grant No. CIT&TCD20180325.


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Ling Xu
    • 1
  • Deng-Shan Wang
    • 1
    Email author
  • Xiao-Yong Wen
    • 1
  • Yao-Lin Jiang
    • 2
  1. 1.School of Applied ScienceBeijing Information Science and Technology UniversityBeijingChina
  2. 2.School of Mathematics and StatisticsXi’an Jiaotong UniversityXi’anChina

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